A351448 -id:A351448 - cp's OEIS frontend

A351442 a(n) = A003958(sigma(n)), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

1, 2, 1, 6, 2, 2, 1, 8, 12, 4, 2, 6, 6, 2, 2, 30, 4, 24, 4, 12, 1, 4, 2, 8, 30, 12, 4, 6, 8, 4, 1, 24, 2, 8, 2, 72, 18, 8, 6, 16, 12, 2, 10, 12, 24, 4, 2, 30, 36, 60, 4, 36, 8, 8, 4, 8, 4, 16, 8, 12, 30, 2, 12, 126, 12, 4, 16, 24, 2, 4, 4, 96, 36, 36, 30, 24, 2, 12, 4, 60, 100, 24, 12, 6, 8, 20, 8

Offset: 1

Antti Karttunen, Feb 12 2022

Question: Are there more fixed points than 1, 2, 8, 128, 288, 720, 32768, 29719872, ..., 2147483648 ?

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to sigma(n)

Cf. A000203, A003958, A322582, A339905, A351443, A351444, A351445, A351446, A351447, A351448, A351456.

Cf. also A348512.

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A351442(n) = A003958(sigma(n));

Multiplicative with a(p^e) = A003958(1 + p + ... + p^e).
a(n) = A003958(A000203(n)).
a(n) = A351444(n) - A322582(n) = A351445(n) + A003958(n).

A351447 Numbers k for which A003958(sigma(k)) = 2*A003958(k), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

Original entry on oeis.org

2, 98, 120, 136, 312, 520, 672, 888, 1080, 1120, 1464, 1480, 1752, 2440, 2520, 2808, 2912, 2920, 3420, 3768, 3848, 4632, 5880, 6048, 6280, 6344, 6552, 6648, 6664, 7512, 7592, 7720, 7992, 8181, 8288, 8892, 9528, 10104, 10968, 11080, 12464, 12520, 12984, 13176, 13664, 14712, 15288

Offset: 1

Antti Karttunen, Feb 12 2022

nonn

Numbers k such that A351442(k) = 2*A003958(k).

In contrast, numbers x for which A064989(sigma(x)) = 2*A064989(x) seem to consist just of {2} followed by A005820: 2, 120, 672, 523776, ..., etc, which (also) contains as its subsequence all the odd terms of A336702 multiplied by 2.

Index entries for sequences related to sigma(n)

Cf. A000203, A003958, A064989, A351442.

Subsequences: A005820 (3-perfect numbers), odd terms of A336702 doubled, the terms of A351443 doubled (2, 98, 81810, ...), A351448 (odd terms in this sequence).

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
isA351447(n) = (A003958(sigma(n))==2*A003958(n));

cp's OEIS Frontend

A351442 a(n) = A003958(sigma(n)), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

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